A145320 - OEIS

%I #18 Jan 17 2024 09:42:41

%S 6727,163472827,3972716635027,96544959500953327,

%T 2346235601819451117727,57018217498871341562048227,

%U 1385656719311335740821444894827,33674229535685863674571412272037527,818351124790581139708098720213611086327

%N Numbers n such that there exists x in N : (x+31)^3-x^3=n^2.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (24302,-1).

%F a(n+2) = 24302*a(n+1)-a(n).

%F G.f.: -6727*x*(x-1) / (x^2-24302*x+1). - _Colin Barker_, Oct 17 2014

%e a(1)=6727 because the first relation is : (682+31)^3-682^3=6727^2.

%t LinearRecurrence[{24302, -1}, {6727, 163472827}, 10] (* _Paolo Xausa_, Jan 17 2024 *)

%o (PARI) Vec(-6727*x*(x-1)/(x^2-24302*x+1) + O(x^20)) \\ _Colin Barker_, Oct 17 2014

%K nonn,easy

%O 1,1

%A _Richard Choulet_, Oct 07 2008

%E a(9) from _Colin Barker_, Oct 17 2014